Three dimensions of
formal languages
Arve Meisingset
Telenor R&D
Dimensions
3. Implementation
1. Denotation
But first,
the language itself
2. Instantiation
The language
as a syntax tree
Population
Name
1
Company
Name
Telenor
Employee
Number
017976
<> Employee
’ Company
’ Population
Person
Name
Arve Meisingset
Person
Name
Arve Meisingset
Labels are local to the superior node
Superior nodes provide the context in an attachment grammar
Graphic notation
isomorphic to alphanumerical notation
Simplification
Population
Company
Company
Emplyee
Person
Emplyee
Person
Even labels and tokens
are syntax trees
Population
Name
1
Company
Name
:
T
e
l
e
n
o
r
Provides lists of significant duplicates
Algorithmic and navigating functions
are subordinate to data
ref. UML class diagrams
Population
Company
Name
Telenor
Employee
Number
017976
<> Employee
’ Company
’ Population
Person
Name
Example
Arve Meisingset
PS. Subordinate, Sequence and Operator form a threedimensional tree; ie. <> and ’ are not needed
with navigating references between the nodes – as an alternative to the Turing tape
1. Denotations
Population
English
Company
Name
Telenor
Denotation
<> Denotation
’ Company
’ English
’ Population
Phenomena
Bedrift
Phenomena
Bedrift
Explisit Isomorphic mapping from Terminologies to Phenomena
The isomorphic mapping is made between inscriptions; there is no need for strings
Phenomena are themselves data inside some observer
Note on modelling
Cir. group
1
Provides overview of
Circuits terminated in the
same two Exchanges
Circuit
Cable pair
Is a Cable pair a physical entity?
Is a Circuit a physical entity
Is Circuit group a physical entity?
Or are they just data providing overview of other data – to serve some tasks?
Do most data model nothing?
2. Instatiations
System
Schema
P <> ’ System (Population
Company
Name
Population
S <> ’ System (Schema
Company
Name
Telenor
Company
Name
Telia
Mappings
from
instances to
classes
Schema and
Population
references
Enforced implicit Homomorphic mapping from Instances to Classes
Graphic notation
with recursion
System
Schema
S
Company
S
Company
Population
Company
Company
Note that class labels
are copied into every instance,
but not every (subordinate) detail
needs be instantiated
Company
Company
Homomorphic
dotted implicit
moppings
Company
Detailed Graphic notation
System
Schema
S
Company
S
Company
Population
Company
Company
The syntax tree
is made up of
lists of lists
with significant duplicates
Company
Company
Company
Note on homomorphism
Implementation
cOMPANY
Company
Instantiation
Languages not satisfying
the homomorphism requirement
are translated to implementations
before instantiation
Company
Ie. Not Class Company
Better Company Class
Best
Company
Company
Company
Note on Subclasses
Company
Employee
Person
Phenomena acting as roles of other phenomena is replacing the
subclass notion
The Schema-Population references are more generic than and
replacing nheritance
Also Contents schemata providing views of Application schemata, have
a similar effect
Also Access control must be much more powerfull than hiding by
classes
3. Implementation
by the Data transformation architecture
Schemata and mappings between schemata
state the rules for transformation of data
between two media
External schemata Application schema
LS
HCI
CS
ETS OS
Internal schemata
ITS DS
Processes
state abstract implementations
PS
DB
•Compiler architecture
•The Application schema provides the domain model inside the
implementation; implementation specifications are added and do not
replace the Application schema
Implementation
System schema
External schema
LS
Layout schema
CS
Contents schema
Application schema
ETS
External terminology schema
OS
Concept schema
ITS
Internal terminology schema
Internal schema
DS
Distribution schema
PS
Physical schema
Implementation
on multiple media
Graphic
Tape
Alfa
DB
SG10 ?
Reports
Process
Tele
Implementation
Note on partial reuse
of more central schemata
Graphic
Tape
Alfa
DB
Reports
Process
Tele
Implementation
Mapping from
External terminology schemata
to
Internal terminology schemata
Company
C1-record
C1-C2-set
C2-record
If a Specification is a Model of an Implementation,
then the Specification has to be Isomorphic to the Implementation
Only change of labels and details are permitted.
Often, as examplified, the mapping is not isomorphic.
We do not require an isomorphic mapping from
Application schemata to Internal schemata,
but the Application schema must itself be in the running implementation
Schemata
can themselves be stored in a database.
Hence, you can have external and internal forms
of each schema
LS CS ETS CS ITS DS PS
External form,
presented to developers
and users
Internal executable form
SG10 ?
Conclusions
UML does neither Model implementations nor anything else
SG10 languages are neither Description techniques for
implementations nor of anything else
Process and Block are internal implementation notions
External HCI aspects are not addressed by SG10
Data(base) aspects are not addressed by SG10
Will competition come from these domains,
and is UML such an approach?